Résumé:

Using a geometrically motivated approach to unsupervised feature extraction, we propose a regularization and generation framework for auto-encoders based on differential geometry. We show that regularizing the variations of auto-encoders with respect to their input yields in a space localized representation useful for a wide range of machine learning tasks. We present an efficient way to approximate the manifold structure of the input signal by building a topological atlas of charts with an auto-encoder . The local chart associated to an input sample is the set of feature vectors spanning the local tangent space to the manifold as approximated by the auto-encoder. In a supervised setting, these charts can be used to encourage the insensitivity of the classifier's output when moving locally along the manifold. Another interesting use of these local charts is the generation of samples from the input distribution in an unsupervised way. The procedure we propose to generate samples exploits the local structure approximated by the auto-encoder to explore efficiently high-dimensional multimodal input distributions. Finally, we relate
auto-encoders to a particular form of non-linear Independent Component Analysis(ICA) and we use this link to propose a novel form of auto-encoder that learns locally independent features.

Jury:
Aaron Courville (président)
Yoshua Bengio (directeur)
Roland Memisevic (membre)

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